Currently having the opposite problem with phones shutting down due to overheating.
But we too have groups of people playing at all hours of the day or night. Raiding parties dashing all over the place. Ever since the raids started, it's actually become quite social, whereas before that, you'd see others playing but no-one really talked much.
The first Legendary event that resulted in Lugia turning up was from 4-7am for us, yet we had 20+ people at the local park doing laps, catching everything we could with every pokestop lured. Doing our bit for the global catch target despite it being 4am in the middle of winter. :-)